STD 11- Mechanical properties of solids PYQs: JEE Mains Physics

Showing 1–50 of 101 questions

1. 1. A copper wire of length \(3\text{ m}\) is stretched by \(3\text{ mm}\) by applying an external force. The volume of the wire is \(600 \times 10^{-6}\text{ m}^3\). The elastic potential energy stored in the wire in stretched condition would be _______ J.
   (Given Young modulus of copper \(= 1.1 \times 10^{11}\text{ N/m}^2\)) 2026 Medium
2. 2. A cube has side length \(5\) cm and modulus of rigidity \(10^5\) N/m\(^2\). The displacement produced by a force of \(10\) N in the upper face of cube is _____ mm. 2026 Medium
3. 3. A metal string \(A\) is suspended from a rigid support and its free end is attached to a block of mass \(M\). Second block having mass \(2M\) is suspended at the bottom of the first block using a string \(B\). The area of cross sections of strings \(A\) and \(B\) are same. The ratio of lengths of strings of \(A\) to \(B\) is \(2\) and the ratio of their Young's moduli \((Y_A/Y_B)\) is \(0.5\). The ratio of elongations in \(A\) to \(B\) is ______. 2026 Medium
4. 4. A string \(A\) of length \(0.314\) m and Young's modulus \(2 \times 10^{10}\) N/m\(^2\) is connected to another string \(B\) of length and Young's modulus both twice of those of \(A\). This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass \(0.8\) kg. The net change in length of the combination is _____ mm. (radius of both the strings is \(0.2\) mm and acceleration due to gravity \(= 10\) m/s\(^2\)) (Mass of both strings is to be neglected as compared to the mass of load) 2026 Hard
5. 5. A uniform wire of length \(l\) of weight \(w\) is suspended from the roof with a weight of \(W\) at the other end. The stress in the wire at \(\dfrac{l}{3}\) distance from the top is \(\left(\dfrac{W}{A} + \dfrac{2}{\gamma}\dfrac{w}{A}\right)\), where, \(A\) is the cross sectional area of the wire. The value of \(\gamma\) is _______. 2026 Medium
6. 6. Figure represents the extension (\(\Delta l\)) of a wire of length \(1\) meter, suspended from the ceiling of the room at one end with a load \(W\) connected to the other end. If the cross-sectional area of the wire is \(10^{-5}\) m\(^2\) then the Young's modulus of the wire is __________ N/m\(^2\).
   2026 Medium
7. 7. The heat extracted out of \(x\) gram of water initially at \(50°C\) to cool it down to \(0°C\) is sufficient to evaporate \((1000 - x)\) gram of water also initially at \(50°C\). The value of \(x\) (closest integer) is _______.
   (Take latent heat of water \(2256\text{ kJ/kg.K}\), specific heat capacity of water \(4200\text{ J/kg.K}\)) 2026 Hard
8. 8. The increase in the pressure required to decrease the volume \((\Delta V)\) of water is \(6.3 \times 10^7\) N/m\(^2\). The percentage decrease in the volume is _____. (Bulk modulus of water \(= 2.1 \times 10^9\) N/m\(^2\).) 2026 Easy
9. 9. The speed of a longitudinal wave in a metallic bar is \(400~m/s.\) If the density and Young's modulus of the bar material are increased by 0.5% and 1% respectively then the speed of the wave is changed approximately to ___________ \(m / s\). 2026 Easy
10. 10. The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus?
    2026 Medium
11. 11. The two wires \(A\) and \(B\) of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire \(A\) and wire \(B\) is \(20/11\). When the joined wire is kept under certain tension the elongations in the wires \(A\) and \(B\) are equal. If the length of wire \(A\) is \(2.2\) m, then the length of wire \(B\) is _______ m. 2026 Medium
12. 12. The Young's modulus of steel wire of radius \(r\) and length \(L\) is \(Y\). If the radius \(r\) and length \(L\) of the wire are doubled then the value of \(Y\) 2026 Easy
13. 13. Two wires \(A\) and \(B\) made of different materials of length 6.0 cm and 5.4 cm, respectively and area of cross sections \(3.0 \times 10^{-5} m^2\) and \(4.5 \times 10^{-5} m^2\), respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of \(A\) to that of \(B\) is \(x : 3\). The value of x is ___________. 2026 Easy
14. 14. Two wires as shown in the figure below, made of steel and have breaking stress of \(12 \times 10^8\) N/m\(^2\). Area of cross-section of upper wire is \(0.008\) cm\(^2\) and of lower wire is \(0.004\) cm\(^2\). The maximum mass that can be added to pan without breaking any wire is _____ kg.
    (take \(g = 10\) m/s\(^2\))
    2026 Hard
15. 15. A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is \(\mathrm{P} \times 10^{11} \mathrm{Nm}^{-2}\), where the value of P is: (Take \(\left.\mathrm{g}=3 \pi \mathrm{~m} / \mathrm{s}^2\right)\) 2025 Medium
16. 16. A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of \(10^5 \mathrm{~N}\) at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement \(\theta\) of the rod axis from its original position would be : (shear moduli, \(\left.\mathrm{G}=10^{10} \mathrm{~N} / \mathrm{m}^2\right)\) 2025 Medium
17. 17. A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of \(0.8 \mathrm{~cm}^3\). If the bulk modulus of the liquid is 2 GPa , the initial volume of the liquid was _______ litre. \(\left(\right.\) Take \(\left.1 \mathrm{~atm}=10^5 \mathrm{~Pa}\right)\) 2025 Medium
18. 18. A steel wire of length 2 m and Young's modulus \(2.0 \times 10^{11} \mathrm{Nm}^{-2}\) is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and \(10^{-3}\) respectively, then the elastic potential energy density of the wire is _______ \(\times 10^5\) (in SI units) 2025 Medium
19. 19. The fractional compression \(\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)\) of water at the depth of 2.5 km below the sea level is ______ \(\%\). Given, the Bulk modulus of water \(=2 \times 10^9 \mathrm{~N} \mathrm{~m}^{-2}\), density of water \(=10^3\) \(\mathrm{kg} \mathrm{m}^{-3}\), acceleration due to gravity \(=\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\). 2025 Medium
20. 20. The increase in pressure required to decrease the volume of a water sample by \(0.2 \%\) is \(\mathrm{P} \times 10^5 \mathrm{Nm}^{-2}\). Bulk modulus of water is \(2.15 \times 10^9 \mathrm{Nm}^{-2}\). The value of P is ________. 2025 Medium
21. 21. The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N , the length of the string is 1.56 m. The original length of the string is _____ m. 2025 Medium
22. 22. The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N , the length of the string is 1.56 m. The original length of the string is _____ m. 2025 Easy
23. 23. The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of \(7 \times 10^6 \mathrm{~Pa}\), would be ____ \(\mathrm{mm}^3\).
    (Given bulk modulus of copper \(=1.4 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\) ) 2025 Easy
24. 24. Two slabs with square cross section of different materials \((1,2)\) with equal sides \((l)\) and thickness \(\mathrm{d}_1\) and \(\mathrm{d}_2\) such that \(\mathrm{d}_2=2 \mathrm{~d}_1\) and \(l \gt \mathrm{d}_2\). Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is \(\theta_2=2 \theta_1\). If the shear moduli of material 1 is \(4 \times 10^9 \mathrm{~N} / \mathrm{m}^2\), then shear moduli of material 2 is \(\mathrm{x} \times 10^9 \mathrm{~N} / \mathrm{m}^2\), where value of \(x\) is ________. 2025 Hard
25. 25. Two wires A and B are made of same material having ratio of lengths \(\frac{L_A}{L_B}=\frac{1}{3}\) and their diameters ratio \(\frac{d_A}{d_B}=2\). If both the wires are stretched using same force, what would be the ratio of their respective elongations? 2025 Easy
26. 26. A material has Poisson's ratio \(0.50.\) If a uniform rod of it suffers a longitudinal strain of \(2 \times {10^{ - 3}}\), then the percentage change in volume is 2024 Medium
27. 27. A wire of cross sectional area \(A\), modulus of elasticity \(2 \times 10^{11} \mathrm{Nm}^{-2}\) and length \(2 \mathrm{~m}\) is stretched between two vertical rigid supports. When a mass of \(2 \mathrm{~kg}\) is suspended at the middle it sags lower from its original position making angle \(\theta=\frac{1}{100}\) radian on the points of support. The value of \(A\) is _______ \(\times 10^{-4} \mathrm{~m}^2\) (consider \(\mathrm{x}<\mathrm{L}\) ). (given: \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )
    2024 Hard
28. 28. A wire of length \(L\) and radius \(r\) is clamped at one end. If its other end is pulled by a force \(F\), its length increases by \(l\). If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become _______. 2024 Hard
29. 29. Each of three blocks \(P\), \(Q\) and \(R\) shown in figure has a mass of \(3 \mathrm{~kg}\). Each of the wire \(A\) and \(B\) has cross-sectional area \(0.005 \mathrm{~cm}^2\) and Young's modulus \(2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\). Neglecting friction, the longitudinal strain on wire \(B\) is _______ \(\times 10^{-4}\). \(\left(\right.\) Take \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )
    2024 Hard
30. 30. Given below are two statements: one is labelled as Assertion\((A)\) and the other is labelled as Reason \((R).\) \(Assertion\) \((A)\) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading. \(Reason\) \((R)\) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling. In the light of the above statements, choose the correct answer from the options given below : 2024 Hard
31. 31. If average depth of an ocean is \(4000 \mathrm{~m}\) and the bulk modulus of water is \(2 \times 10^9 \mathrm{Nm}^{-2}\), then fractional compression \(\frac{\Delta V}{V}\) of water at the bottom of ocean is \(\alpha \times 10^{-2}\). The value of \(\alpha\) is ___________(Given, \(\mathrm{g}=10 \mathrm{~ms}^{-2}, \rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}\) ) 2024 Hard
32. 32. One end of a metal wire is fixed to a ceiling and a load of \(2 \mathrm{~kg}\) hangs from the other end. A similar wire is attached to the bottom of the load and another load of \(1 \mathrm{~kg}\) hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be _______. [Area of cross section of wire \(=0.005 \mathrm{~cm}^2\), \(\mathrm{Y}=2 \times 10^{11}\  \mathrm{Nm}^{-2}\) and \(\left.\mathrm{g}=10 \mathrm{~ms}^{-2}\right]\) 2024 Hard
33. 33. The density and breaking stress of a wire are \(6 \times\) \(10^4 \mathrm{~kg} / \mathrm{m}^3\) and \(1.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2\) respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is \(\frac{1^{\text {rd }}}{3}\) of the value on the surface of earth. The maximum length of the wire with breaking is _______ \(\mathrm{m}\) (take, \(\mathrm{g}=\) \(\left.10 \mathrm{~m} / \mathrm{s}^2\right)\) 2024 Hard
34. 34. The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by \(0.02 \%\) is ______ \(\mathrm{m}\). (Take density of sea water \(=10^3 \mathrm{kgm}^{-3}\), Bulk modulus of rubber \(=9 \times 10^8 \mathrm{Nm}^{-2}\), and \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) ) 2024 Hard
35. 35. Two blocks of mass \(2 \mathrm{~kg}\) and \(4 \mathrm{~kg}\) are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is \(4.0 \times 10^{-5}\) \(\mathrm{m}\) and Young's modulus of the metal is \(2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^2\). The longitudinal strain developed in the wire is \(\frac{1}{\alpha \pi}\). The value of \(\alpha\) is _______. [Use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )
    2024 Hard
36. 36. Two metallic wires \(P\) and \(Q\) have same volume and are made up of same material. If their area of cross sections are in the ratio \(4: 1\) and force \(F_1\) is applied to \(\mathrm{P}\), an extension of \(\Delta l\) is produced. The force which is required to produce same extension in \(Q\) is \(\mathrm{F}_2\).The value of \(\frac{\mathrm{F}_1}{\mathrm{~F}_2}\) is _______. 2024 Hard
37. 37. Two persons pull a wire towards themselves. Each person exerts a force of \(200 \mathrm{~N}\) on the wire. Young's modulus of the material of wire is \(1 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\). Original length of the wire is \(2 \mathrm{~m}\) and the area of cross section is \(2 \mathrm{~cm}^2\). The wire will extend in length by _______ \(\mu \mathrm{m}\). 2024 Hard
38. 38. With rise in temperature, the Young's modulus of elasticity _______. 2024 Hard
39. 39. Young's modulus is determined by the equation given by \(\mathrm{Y}=49000 \frac{\mathrm{m}}{\ell} \frac{\text { dyne }}{\mathrm{cm}^2}\) where \(\mathrm{M}\) is the mass and \(\ell\) is the extension of wre used in the experiment. Now error in Young modules \((\mathrm{Y})\) is estimated by taking data from \(M-\ell\) plot in graph paper. The smallest scale divisions are \(5 \mathrm{~g}\) and \(0.02\) \(\mathrm{cm}\) along load axis and extension axis respectively. If the value of \(M\) and \(\ell\) are \(500 \mathrm{~g}\) and \(2 \mathrm{~cm}\) respectively then percentage error of \(\mathrm{Y}\) is _______. 2024 Hard
40. 40. Young's modules of material of a wire of length '\(L\)' and cross-sectional area \(A\) is \(Y\). If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be _______. 2024 Hard
41. 41. A \(100\,m\) long wire having cross-sectional area \(6.25 \times 10^{-4}\,m ^2\) and Young's modulus is \(10^{10}\,Nm ^{-2}\) is subjected to a load of \(250\,N\), then the elongation in the wire will be : 2023 Easy
42. 42. A certain pressure \(P\) is applied to \(1\) litre of water and \(2\) litre of a liquid separately. Water gets compressed to \(0.01 \%\) whereas the liquid gets compressed to \(0.03 \%\). The ratio of Bulk modulus of water to that of the liquid is \(\frac{3}{x}\). The value of \(x\) is \(...........\) 2023 Medium
43. 43. A force is applied to a steel wire ' \(A\) ', rigidly clamped at one end. As a result elongation in the wire is \(0.2\,mm\). If same force is applied to another steel wire ' \(B\) ' of double the length and a diameter \(2.4\) times that of the wire ' \(A\) ', the elongation in the wire ' \(B\) ' will be \(............\times 10^{-2}\,mm\) (wires having uniform circular cross sections) 2023 Medium
44. 44. A metal block of mass \(m\) is suspended from a rigid support through a metal wire of diameter \(14\,mm\). The tensile stress developed in the wire under equilibrium state is \(7 \times 10^5\,Nm ^{-2}\). The value of mass \(m\) is \(......kg\). (Take, \(g =9.8\,ms ^{-2}\) and \(\left.\pi=\frac{22}{7}\right)\) 2023 Medium
45. 45. A steel rod has a radius of \(20\,mm\) and a length of \(2.0\,m\). A force of \(62.8\,kN\) stretches it along its length. Young's modulus of steel is \(2.0 \times 10^{11}\,N / m ^2\). The longitudinal strain produced in the wire is \(..........\times 10^{-5}\) 2023 Easy
46. 46. A wire of length \(L\) and radius \(r\) is clamped rigidly at one end. When the other end of the wire is pulled by a force \(f\), its length increases by \(l\). Another wire of same material of length \(2 L\) and radius \(2 r\) is pulled by a force \(2 f\). Then the increase in its length will be 2023 Medium
47. 47. An aluminium rod with Young's modulus \(Y =7.0\) \(\times 10^{10} N / m ^2\) undergoes elastic strain of \(0.04 \%\). The energy per unit volume stored in the rod in SI unit is: 2023 Easy
48. 48. As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of \(45^{\circ}\) with the load axis. The length of wire is \(62.8\,cm\) and its diameter is \(4\,mm\). The Young's modulus is found to be \(x \times\) \(10^4\,Nm ^{-2}\). The value of \(x\) is
    2023 Easy
49. 49. Choose the correct relationship between Poisson ratio \((\sigma)\). bulk modulus \(( K )\) and modulus of rigidity \((\eta)\) of a given solid object: 2023 Medium
50. 50. Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A\): Steel is used in the construction of buildings and bridges. Reason \(R:\) Steel is more elastic and its elastic limit is high. In the light of above statements, choose the most appropriate answer from the options given below 2023 Easy

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